Data center waste heat compensation system regulation and control strategy considering adjustable data load

Abstract

The invention relates to a data center waste heat compensation system regulation and control strategy considering an adjustable data load, and aims to solve the problem of system heat energy supply and demand mismatching caused by the fact that a combined heat and power generation unit adopts an operation mode of setting heat by electricity under the background of taking central heating as a main heating means. Analyzing the flexible adjustment capability of the data load, constructing a data load model with uncertainty, and calculating the operation power of the server; according to thermal load characteristics of community users and heat production characteristics of a data center server, a thermal compensation system working model with data center waste heat as a heat source is established, and a Tube model prediction control strategy is adopted to regulate and control the model; and finally, through example verification, the regulation and control strategy provided by the invention effectively improves the economical efficiency of the operation of the heating system while inhibiting the influence of the data load uncertainty.

Description

Technical Field

[0001] The present invention relates to the field of optimization and regulation of clean heating systems, and in particular to a regulation strategy for a waste heat compensation system of a data center taking into account an adjustable data load. Background Art

[0002] Under the guidance of the "dual carbon" goal, green, low-carbon, energy conservation and consumption reduction have gradually become a consensus of the whole society. my country's energy system is at a critical juncture of green and low-carbon transformation, and it is urgent to establish a clean, efficient and flexible energy structure system. The heating system is an important part of the energy system. Using waste heat from production and life to compensate for traditional heating has important research significance for improving energy utilization efficiency and promoting environmental protection transformation of the system. Summary of the invention

[0003] Aiming at the problem of mismatch between system heat supply and heat load demand caused by the operation of cogeneration units in the mode of "electricity determines heat" under the background of centralized heating as the main heating means, the present invention innovatively proposes a control strategy for the waste heat compensation system of a data center considering adjustable data load, constructs an operation optimization model of the waste heat compensation system of a data center, and adopts Tube-MPC to control the waste heat output, thereby achieving the heating goal while ensuring the economy and environmental protection of the system.

[0004] The technical solution to implement the present invention is: a data center waste heat compensation system control strategy considering adjustable data load, and its specific steps are as follows:

[0005] 1) Modeling server power considering the time-adjustable characteristics of data load

[0006] 1.1) Data load model

[0007] During operation, the data center will receive two types of data loads: interactive (IN) and batch processing (BA). The interactive load is sensitive to delay and requires the data center to process it immediately, so it does not have the ability to adjust the time; the batch processing load monomer has a large amount of computing data and the processing time can be from several minutes to several days. It has obvious delay tolerance characteristics and can be adjusted on the time scale.

[0008] Under the guidance of the operator's incentives, data center users agree that BA-type loads are adjusted, provide specific load information after unified processing of requirements, and then participate in the optimization and regulation of the system. The amount of adjustment in BA-type loads is regarded as the response amount, which can be expressed as:

[0009]

[0010]

[0011] Where: k∈{0,1,…,k,…,N k},N k is the total number of time periods in a complete regulation cycle; is the response of BA type load at time k; φ ba (k) is the BA load received by the data center at time k; β ba is the proportion of batch processing load in the total data load; is the total load received by the data center at time k, which will change with the data processing needs of the data center users and is uncertain. Its distribution range is

[0012] The time transfer of BA type load is reflected in that the data load can be transferred from the current period to other periods, and data processing only needs to be completed within the specified time window. The model definition is as follows:

[0013]

[0014] Where: is the BA load response transferred from time k to time period [k+1,T], and the left side of the equation is the distribution of the adjusted BA load response in different time periods.

[0015] In summary, the BA load λ processed by the data center at time k ba (k) and IN type load λ in (k) can be expressed as:

[0016]

[0017]

[0018] In order to ensure the quality of service when processing data load, the response time for processing data load is required not to exceed the specified maximum delay that users can tolerate. Assuming that the data load is evenly distributed during runtime, according to the M / M / 1 queuing theory, it can be expressed as:

[0019]

[0020]

[0021]

[0022] Where: T qt Waiting time in queue for data load; n ser (k) is the number of servers in the power-on state at time k; T ht is the data load processing time; μ is the server processing rate; The maximum delay that the user can tolerate.

[0023] Formula (1) to (8) analyze the time transferability of data load. Under the premise of satisfying the data load service quality, the data load of the data center can be adjusted on a time scale according to different goals.

[0024] 1.2) Server Power Model

[0025] The active power of a data center server is mainly determined by the number of servers powered on during the current period and the amount of data load being processed. Since data load has the characteristic of time transferability, the active power of the server can be changed by adjusting the data load, thereby changing the waste heat generated.

[0026] For simplicity, this paper assumes that all servers in the data center are of the same model and that the control center evenly distributes the data load to all powered-on servers at any time. The active power of data center servers under different working conditions, the number of powered-on servers, and the server CPU utilization constraints can be expressed as:

[0027]

[0028]

[0029]

[0030] Where: P ser (k) is the active power of the server in the data center at time k; P idle is the silent power of a single server when it is not processing data load; P peak is the peak power; φ(k) is the data load at time k without considering uncertainty; μ is the server processing rate; Indicates the maximum number of available servers. max Indicates the upper limit of CPU usage of a single server.

[0031] 2) Working model of data center waste heat compensation system

[0032] The data center waste heat compensation system uses the data center waste heat as the heat source. In order to determine the waste heat recovery amount at each moment, the dynamic indoor temperature of the data center should be analyzed. The indoor temperature of the data center is affected by the heat emitted by the server, the cooling power of the refrigeration system, and the outdoor temperature. Considering that the data center building is usually a windowless closed structure, its building structure and servers are abstracted to form a resistant capacitance (RC) thermal network model.

[0033] The RC heat network model of the data center abstracts the entities in the building into heat network nodes, uses the heat capacity of each node to represent the heat storage capacity, and the thermal resistance between nodes to represent the heat transfer path. The RC heat network model of the data center contains 5 nodes: ewo 、External wall inner node X ewi 、Inner wall node X iw 、Server Node X r and air node X ia .

[0034] The relationship between the temperature of each node and the temperature of the adjacent nodes and the injected heat in the RC thermal network model of the data center can be expressed by a first-order differential equation:

[0035]

[0036] Where: m nodes are nodes to be described; T m and T n are the m and n node temperatures respectively; C m is the heat capacity of node m; R n,m is the thermal resistance between nodes n and m; H m is the external heat input to the m node; Ω c is the set of adjacent nodes of node m.

[0037] According to formula (12), the first-order differential equations corresponding to the five nodes in the RC heating network are listed as shown in formulas (13)-(17).

[0038]

[0039]

[0040]

[0041]

[0042]

[0043] Where: T ewo is the temperature of the outer wall; T ewi is the temperature inside the exterior wall; T ia is the indoor air temperature; T iw is the inner wall temperature; T r is the server rack temperature; R oos is the thermal resistance of the exterior wall; R ewo is the half value of thermal resistance of the outer layer of the exterior wall; R ewi is the half value of the thermal resistance of the inner layer of the exterior wall; R ois is the thermal resistance of the inner surface of the exterior wall; R iws is the thermal resistance of the inner wall surface; R iw is the thermal resistance of the inner wall; R cis the thermal resistance of the ceiling; R r is the thermal resistance of the data center server equipment; C ewo is the heat capacity of the outer layer of the exterior wall; C ewi is the heat capacity of the inner layer of the exterior wall; C iw is the heat capacity of the inner wall; C r Heat capacity for data center server equipment; C ia is the heat capacity of the air in the computer room; T o is the outdoor air temperature, H e is the heat gain of the building envelope, T o and H e It is determined by the outdoor environment and directly affects the internal temperature of the data center. It can be calculated based on the indoor and outdoor environmental data. c is the cooling power of the refrigeration system at time k; H I ' T (k) is the waste heat generated by the server at time k.

[0044] The waste heat generation of the server is calculated as follows:

[0045] H I ' T (k) = H IT (k)+ΔH(k) (18)

[0046] H IT (k) = η IT P ser (k) (19)

[0047] Where: H IT (k) is the heat dissipated by the server when the data load uncertainty is not considered at time k; ΔH is the change in server residual heat caused by data load uncertainty; η IT is the dissipation rate of the server. Since the power consumed by the server is almost completely converted into heat, the dissipation rate η IT Set to 1.

[0048] In the cooling system of the data center, the condenser where heat is concentrated is a good location for waste heat recovery. The refrigerant absorbs the heat generated by the server in the evaporator, is cooled in the condenser, and releases the heat it carries. On this basis, according to the cooling power H of the cooling system at time k, c (k), the waste heat H recovered at each time in the data center can be calculated DC (k):

[0049]

[0050] H DC (k) = η DC H c (k) (21)

[0051] Where: P acs (k) is the active power of the data center cooling system at time k; η acs is the energy efficiency coefficient of the refrigeration system; The capacity of air conditioning equipment configured for the data center; η DC Indicates waste heat recovery efficiency.

[0052] The waste heat collected by the data center is usually low-grade waste heat and cannot be directly used for heating systems. In order to meet the prerequisites, the low-temperature waste heat needs to be upgraded through a heat pump, which can be expressed as:

[0053] H HP (k) = H DC (k)+P HP (k) (22)

[0054] H HP (k) = COP HP P HP (k) (23)

[0055] Where: H HP (k) is the available high-grade thermal power output by the heat pump at time k; P HP (k) is the electrical power consumed by the heat pump at time k; COP HP is the coefficient of performance of the heat pump.

[0056] The heat storage tank is used to store the waste heat collected from the data center. The heat energy Q stored in the recovery stage DC It can be expressed as:

[0057]

[0058] Where: k c It is the end time of the heat storage phase of the waste heat recovery system.

[0059] During the working stage of the waste heat compensation system in the data center, the heat storage tank exchanges heat with the heating medium through the heat exchanger. This dynamic process can be expressed as:

[0060]

[0061]

[0062] Where: M qms M is the mass of heat medium in the heat storage tank; g is the quality of heating medium; C qms C is the constant pressure specific heat capacity of the heat transfer medium in the heat exchanger connected to the heat storage tank; g is the constant pressure specific heat capacity of the heating medium; m qms is the mass flow rate of the heat exchange medium in the heat exchanger connected to the heat storage tank; m gis the mass flow rate of heating medium; T mi (k) is the inlet temperature of the heat exchanger connected to the heat storage tank at time k; T mo (k) is the outlet temperature of the heat exchanger connected to the heat storage tank at time k; T gim (k) is the inlet temperature of the heating medium that exchanges heat energy with the data center cooling system at time k; T gom (k) is the outlet temperature of the heating medium that exchanges heat energy with the data center cooling system at time k.

[0063] After discretizing equations (13)-(17) and integrating them with equations (25) and (26), the spatial state equation of the data center waste heat compensation system can be obtained:

[0064]

[0065] Where: x = [T ewo T ewi T ia T iw T r T co T goc ] T is the state variable; u=[T o H e -H c H IT m csr m g ] T is the control variable; r=[ΔH] T is the disturbance variable.

[0066] The coefficient matrices A, B, C and F of the data center waste heat compensation system are as follows.

[0067]

[0068]

[0069]

[0070] F = [0000100] T (31)

[0071] 3) Data center waste heat compensation system control strategy

[0072] This section proposes a control strategy for the waste heat compensation system in a data center. With the goal of minimizing the total cost of community users, Tube-MPC is used to optimize the system based on the price signals of various costs and the heat load requirements of community users.

[0073] 3.1) Objective Function

[0074] When optimizing the heating process, it is necessary to consider the electricity purchase cost W of community users. E (k), heat purchase cost W H (k) Environmental value cost W ENV (k) and the subsidy cost W for guiding data center users to actively respond to the subsidy IT (k), so the objective function can be expressed as:

[0075]

[0076] Where: W is the total daily operating cost, k0 is the starting time of optimization control.

[0077] The costs can be expressed as:

[0078]

[0079] Where: c e (k) is the unit electricity price at time k; p e (k) is the power purchased by the community users at time k; c h (k) is the unit price of heat purchased at time k; p h (k) is the heat purchase power of community users at time k; q wh (k) is the unit price of waste heat in the data center at time k; p wh (k) is the waste heat power purchased by the user from the data center operator at time k; They are the CO2 emission intensity per unit of production capacity of traditional thermal power plants; is the environmental value of unit CO2; q ba (k) is the unit incentive given by the data center to the BA load at time k; q ba The value range of (k) is in It is the upper limit of the excitation for BA type load.

[0080] 3.2) Constraints

[0081] 1. Data center indoor temperature constraints:

[0082]

[0083] Where: They respectively represent the upper and lower limits of the allowed indoor temperature in the data center.

[0084] 2. Thermal energy supply and demand mismatch constraints

[0085] P min ≤P(k)≤P max (35)

[0086]

[0087] Where: P(k) is the degree of mismatch between heat supply and demand at time k; p load (k) is the heat load demand of community users at time k; γ is the rated heat-to-electricity ratio of the cogeneration unit; P min , P max are the minimum and maximum values ​​of the allowed mismatch between heat supply and demand, respectively.

[0088]

[0089] Where: T n It is the time period of thermal and electric load mismatch during the system operation cycle; The longest time period of thermal and electrical load mismatch to ensure normal operation of the system within a complete cycle.

[0090] 3. Thermal comfort constraints for community users

[0091] During the optimization and control process, the indoor temperature of community users should be guaranteed to meet the thermal comfort requirements of the human body:

[0092]

[0093] Where: T user (k) is the indoor temperature of the community users at time k; and They are the minimum and maximum values ​​of standard indoor temperature respectively.

[0094] 4. Heat storage tank heat storage constraints

[0095] 0≤Q DC (k)≤Q max (39)

[0096] Where: Q max is the upper limit of heat storage of the phase change heat storage tank.

[0097] 3.3) Tube-MPC control strategy

[0098] In order to reduce the impact of data load uncertainty on the system during the optimization and control process, this paper adopts the Tube-MPC optimization and control method. Tube-MPC consists of a nominal model predictive controller and an auxiliary feedback controller, which transforms the control of the actual system into the control of the nominal system, so that the trajectory of the uncertain system is always in the Tube centered on the nominal trajectory. The actual uncertain data center waste heat compensation system is x(k+1)=Ax(k)+Bu(k)+Fr(k), and the constraints of the state variable x and the control variable u are x∈X,u∈U; the corresponding undisturbed nominal data center waste heat compensation system is z(k+1)=Az(k)+Bv(k), and the constraints of the state variable z and the control variable v are z∈Z,v∈V.

[0099] The nominal model predictive controller needs to control the nominal data center waste heat compensation system according to the objective function (32) to generate the economically optimal state trajectory {z(0),z(1),…,z(N)}, where z(N)∈Z N , N is the prediction time domain, Z N is the terminal contraction state constraint set, The nominal system constraints are more stringent than the actual system and can be expressed as:

[0100] Z=k1X,V=k2U,k1,k2∈(0,1) (40)

[0101] Where: k1 and k2 are the adjustment parameters of the controller. By adjusting k1 and k2, the constraint set can be tightened.

[0102] The goal of the auxiliary feedback controller is to generate a set of control actions u to control the actual data center residual heat compensation system with uncertainty, minimizing the deviation between the actual data center residual heat compensation system state trajectory {x(0), x(1), ..., x(N)} and the optimal trajectory {z(0), z(1), ..., z(N)} obtained by the nominal model predictive controller. The objective function needs to ensure that the output and input (y and u) of the auxiliary feedback controller follow the output and input (g and v) of the nominal model predictive controller, and the constraints of the state and input are not tightened, which are X and U respectively. The objective function can be expressed as follows:

[0103]

[0104] Where: y = Cx, g = Cv; α and β are the weights of the controller output and input, respectively. α = 1 and β = 0.01 are usually selected to prioritize tracking the output generated by the nominal model predictive controller.

[0105] This paper calls MPT in Matlab to solve the optimization control problem.

[0106] The beneficial effects of the data center waste heat compensation system control strategy considering adjustable data load of the present invention are as follows:

[0107] 1. The time transferability of data load is analyzed, and the waste heat of data center based on data load is modeled. While fully exploring the adjustable capacity of data center waste heat on time scale, it promotes waste heat consumption and improves the economy of the system.

[0108] 2. In response to the mismatch between heat supply and demand of the system during heating, this paper comprehensively considers the waste heat supply of the data center and the heat load demand of community users, regulates the waste heat output by the waste heat compensation system of the data center in time, and transfers 70.59% of the waste heat to the period with higher heat load demand, thus making up for the shortage of heat energy.

[0109] 3. Based on the Tube-MPC control method, the control of the actual data center waste heat compensation system is transformed into the control of the nominal system, and the trajectory of the actual disturbed system is guided into the Tube centered on the nominal trajectory, which reduces the impact of data load uncertainty on the system and improves the stability of system operation. BRIEF DESCRIPTION OF THE DRAWINGS

[0110] Figure 1 It is a schematic diagram of the waste heat compensation system of a data center;

[0111] Figure 2 It is a schematic diagram of the time shift of data load;

[0112] Figure 3 This is a schematic diagram of the RC heating network model of the data center;

[0113] Figure 4 It is a schematic diagram of the complete optimization and control process;

[0114] Figure 5 It is a schematic diagram of the typical daily data load variation curve;

[0115] Figure 6 It is a schematic diagram of the outdoor temperature variation curve on a typical day;

[0116] Figure 7 This is a diagram of the data load and the number of servers powered on in Example 1;

[0117] Figure 8 This is a diagram of the data load and the number of servers powered on in Example 2;

[0118] Fig. 9 This is a diagram of the data load and the number of servers powered on in Example 3;

[0119] Fig.10 is a schematic diagram of thermal power and thermal load requirements under Example 1;

[0120] Fig.11 This is a schematic diagram of thermal power and thermal load requirements under Example 2;

[0121] Fig.12 This is a schematic diagram of thermal power and thermal load requirements under Example 3;

[0122] Fig.13 It is a statistical diagram of heating effects of each example;

[0123] Fig.14 It is a schematic diagram of the system state trajectory;

[0124] Fig.15 This is a schematic diagram of the comparison results under Tube-MPC and MPC; DETAILED DESCRIPTION

[0125] The following is combined with Figure 1-15 The present invention is further described in detail with specific implementation modes, and the specific implementation modes described herein are only used to explain the present invention and are not used to limit the present invention.

[0126] 1. Data Center Waste Heat Compensation System Operation Framework

[0127] This paper takes the heating system involving waste heat from data centers as the research object and constructs the operation framework of the waste heat compensation system of data centers. Figure 1 As shown, the data center waste heat compensation system mainly includes a data center with a waste heat recovery device, a heat pump, a heat storage tank and a heat exchanger.

[0128] The servers in the data center will emit heat when processing data loads. The refrigeration system with waste heat recovery device recovers the waste heat and keeps the indoor temperature of the data center within the specified range. The recovered waste heat is upgraded by the heat pump and stored in the heat storage tank. During the heating stage, in order to alleviate the mismatch between heat supply and demand, the waste heat output by the waste heat compensation system of the data center is adjusted. At the same time, community users pay subsidies to the data center operator to encourage and guide data center users to formulate adjustment plans for the load and provide their own data load information, agreeing that part of the load will be adjusted. On this basis, the adjusted load is transferred to the period with large heat shortage to increase the waste heat.

[0129] 2. Server Power Modeling Considering the Time-Adjustable Characteristics of Data Load

[0130] Data centers consume electrical energy when processing data loads, and their active power is related to the amount of data load. This section constructs a data load model with uncertainty, characterizes its adjustment ability on a time scale, determines the amount of data load at each moment, and then obtains the active power of the server as the basis for subsequent calculation of server waste heat.

[0131] 2.1 Data Load Model

[0132] During operation, the data center will receive two types of data loads: interactive (IN) and batch processing (BA). The interactive load is sensitive to delay and requires the data center to process it immediately, so it does not have the ability to adjust the time; the batch processing load monomer has a large amount of computing data and the processing time can be from several minutes to several days. It has obvious delay tolerance characteristics and can be adjusted on the time scale.

[0133] Under the guidance of the operator's incentives, data center users agree that BA-type loads are adjusted, provide specific load information after unified processing of requirements, and then participate in the optimization and regulation of the system. The amount of adjustment in BA-type loads is regarded as the response amount, which can be expressed as:

[0134]

[0135]

[0136] Where: k∈{0,1,…,k,…,N k},N k is the total number of time periods in a complete regulation cycle; is the response of BA type load at time k; φ ba (k) is the BA load received by the data center at time k; β ba is the proportion of batch processing load in the total data load; is the total load received by the data center at time k, which will change with the data processing needs of the data center users and is uncertain. Its distribution range is

[0137] The time transfer of BA type load is reflected in that the data load can be transferred from the current period to other periods, and data processing only needs to be completed within the specified time window. The model definition is as follows:

[0138]

[0139] Where: is the BA load response transferred from time k to time period [k+1,T], and the left side of the equation is the distribution of the adjusted BA load response in different time periods.

[0140] In summary, the BA load λ processed by the data center at time k ba (k) and IN type load λ in (k) can be expressed as:

[0141]

[0142]

[0143] In order to ensure the quality of service when processing data load, the response time for processing data load is required not to exceed the specified maximum delay that users can tolerate. Assuming that the data load is evenly distributed during runtime, according to the M / M / 1 queuing theory, it can be expressed as:

[0144]

[0145]

[0146]

[0147] Where: T qt Waiting time in queue for data load; n ser (k) is the number of servers in the power-on state at time k; T ht is the data load processing time; μ is the server processing rate; The maximum delay that the user can tolerate.

[0148] Formulas (1) to (8) analyze the time transferability of data load. Under the premise of satisfying the data load service quality, the data load of the data center can be adjusted on a time scale according to different goals. Figure 2 shown.

[0149] 2.2 Server Power Model

[0150] The active power of a data center server is mainly determined by the number of servers powered on during the current period and the amount of data load being processed. Since data load has the characteristic of time transferability, the active power of the server can be changed by adjusting the data load, thereby changing the waste heat generated.

[0151] For simplicity, this paper assumes that all servers in the data center are of the same model and that the control center evenly distributes the data load to all powered-on servers at any time. The active power of data center servers under different working conditions, the number of powered-on servers, and the server CPU utilization constraints can be expressed as:

[0152]

[0153]

[0154]

[0155] Where: P ser (k) is the active power of the server in the data center at time k; P idle is the silent power of a single server when it is not processing data load; P peak is the peak power; φ(k) is the data load at time k without considering uncertainty; μ is the server processing rate; Indicates the maximum number of available servers. max Indicates the upper limit of CPU usage of a single server.

[0156] Green Certificate Trading Model for Inter-regional Interconnection System

[0157] 3. Working Model of Data Center Waste Heat Compensation System

[0158] The data center waste heat compensation system uses the data center waste heat as the heat source. In order to determine the waste heat recovery amount at each moment, the dynamic indoor temperature of the data center should be analyzed. The indoor temperature of the data center is affected by the heat dissipated by the server, the cooling power of the refrigeration system, and the outdoor temperature. Considering that the data center building is usually a windowless closed structure, its building structure and servers are abstracted to form a resistant capacitance (RC) thermal network model, such as Figure 3 shown.

[0159] The RC heat network model of the data center abstracts the entities in the building into heat network nodes, uses the heat capacity of each node to represent the heat storage capacity, and the thermal resistance between nodes to represent the heat transfer path. The RC heat network model of the data center contains 5 nodes: ewo 、External wall inner node X ewi 、Inner wall node X iw 、Server Node X r and air node X ia .

[0160] The relationship between the temperature of each node and the temperature of the adjacent nodes and the injected heat in the RC thermal network model of the data center can be expressed by a first-order differential equation:

[0161]

[0162] Where: m nodes are nodes to be described; T m and T n are the m and n node temperatures respectively; C m is the heat capacity of node m; R n,m is the thermal resistance between nodes n and m; H m is the external heat input to the m node; Ω c is the set of adjacent nodes of node m.

[0163] According to formula (12), the first-order differential equations corresponding to the five nodes in the RC heating network are listed as shown in formulas (13)-(17).

[0164]

[0165]

[0166]

[0167]

[0168]

[0169] Where: T ewo is the temperature of the outer wall; T ewi is the temperature inside the exterior wall; T ia is the indoor air temperature; T iw is the inner wall temperature; T r is the server rack temperature; R oos is the thermal resistance of the exterior wall; R ewo is the half value of thermal resistance of the outer layer of the exterior wall; R ewi is the half value of the thermal resistance of the inner layer of the exterior wall; R ois is the thermal resistance of the inner surface of the exterior wall; R iws is the thermal resistance of the inner wall surface; R iw is the thermal resistance of the inner wall; R c is the thermal resistance of the ceiling; R r is the thermal resistance of the data center server equipment; C ewo is the heat capacity of the outer layer of the exterior wall; C ewi is the heat capacity of the inner layer of the exterior wall; C iw is the heat capacity of the inner wall; C r Heat capacity for data center server equipment; C ia is the heat capacity of the air in the computer room; T o is the outdoor air temperature, H e is the heat gain of the building envelope, T o and H e It is determined by the outdoor environment and directly affects the internal temperature of the data center. It can be calculated based on the indoor and outdoor environmental data. c is the cooling power of the refrigeration system at time k; H I ' T (k) is the waste heat generated by the server at time k.

[0170] The waste heat generation of the server is calculated as follows:

[0171] H I ' T (k) = H IT (k)+ΔH(k) (18)

[0172] H IT (k) = η IT P ser (k) (19)

[0173] Where: H IT(k) is the heat dissipated by the server when the data load uncertainty is not considered at time k; ΔH is the change in server residual heat caused by data load uncertainty; η IT is the dissipation rate of the server. Since the power consumed by the server is almost completely converted into heat, the dissipation rate η IT Set to 1.

[0174] In the cooling system of the data center, the condenser where heat is concentrated is a good location for waste heat recovery. The refrigerant absorbs the heat generated by the server in the evaporator, is cooled in the condenser, and releases the heat it carries. On this basis, according to the cooling power H of the cooling system at time k, c (k), the waste heat H recovered at each time in the data center can be calculated DC (k):

[0175]

[0176] H DC (k) = η DC H c (k) (21)

[0177] Where: P acs (k) is the active power of the data center cooling system at time k; η acs is the energy efficiency coefficient of the refrigeration system; The capacity of air conditioning equipment configured for the data center; η DC Indicates waste heat recovery efficiency.

[0178] The waste heat collected by the data center is usually low-grade waste heat and cannot be directly used for heating systems. In order to meet the prerequisites, the low-temperature waste heat needs to be upgraded through a heat pump, which can be expressed as:

[0179] H HP (k) = H DC (k)+P HP (k) (22)

[0180] H HP (k) = COP HP P HP (k) (23)

[0181] Where: H HP (k) is the available high-grade thermal power output by the heat pump at time k; P HP (k) is the electrical power consumed by the heat pump at time k; COP HP is the coefficient of performance of the heat pump.

[0182] The heat storage tank is used to store the waste heat collected from the data center. The heat energy Q stored in the recovery stage DC It can be expressed as:

[0183]

[0184] Where: k c It is the end time of the heat storage phase of the waste heat recovery system.

[0185] During the working stage of the waste heat compensation system in the data center, the heat storage tank exchanges heat with the heating medium through the heat exchanger. This dynamic process can be expressed as:

[0186]

[0187]

[0188] Where: M qms M is the mass of heat medium in the heat storage tank; g is the quality of heating medium; C qms C is the constant pressure specific heat capacity of the heat transfer medium in the heat exchanger connected to the heat storage tank; g is the constant pressure specific heat capacity of the heating medium; m qms is the mass flow rate of the heat exchange medium in the heat exchanger connected to the heat storage tank; m g is the mass flow rate of heating medium; T mi (k) is the inlet temperature of the heat exchanger connected to the heat storage tank at time k; T mo (k) is the outlet temperature of the heat exchanger connected to the heat storage tank at time k; T gim (k) is the inlet temperature of the heating medium that exchanges heat energy with the data center cooling system at time k; T gom (k) is the outlet temperature of the heating medium that exchanges heat energy with the data center cooling system at time k.

[0189] After discretizing equations (13)-(17) and integrating them with equations (25) and (26), the spatial state equation of the data center waste heat compensation system can be obtained:

[0190]

[0191] Where: x = [T ewo T ewi T ia T iw T r T co T goc ] T is the state variable; u=[T o H e -H c H IT m csr m g ] T is the control variable; r=[ΔH] Tis the disturbance variable.

[0192] The coefficient matrices A, B, C and F of the data center waste heat compensation system are as follows.

[0193]

[0194]

[0195]

[0196] F = [0000100] T (31)

[0197] 4. Data Center Waste Heat Compensation System Control Strategy

[0198] 4.1 Objective Function

[0199] When optimizing the heating process, it is necessary to consider the electricity purchase cost W of community users. E (k), heat purchase cost W H (k) Environmental value cost W ENV (k) and the subsidy cost W for guiding data center users to actively respond to the subsidy IT (k), so the objective function can be expressed as:

[0200]

[0201] Where: W is the total daily operating cost, k0 is the starting time of optimization control.

[0202] The costs can be expressed as:

[0203]

[0204] Where: c e (k) is the unit electricity price at time k; p e (k) is the power purchased by the community users at time k; c h (k) is the unit price of heat purchased at time k; p h (k) is the heat purchase power of community users at time k; q wh (k) is the unit price of waste heat in the data center at time k; p wh (k) is the waste heat power purchased by the user from the data center operator at time k; They are the CO2 emission intensity per unit of production capacity of traditional thermal power plants; is the environmental value of unit CO2; q ba (k) is the unit incentive given by the data center to the BA load at time k; q ba The value range of (k) is in It is the upper limit of the excitation for BA type load.

[0205] 4.2 Constraints

[0206] 1. Data center indoor temperature constraints:

[0207]

[0208] Where: They respectively represent the upper and lower limits of the allowed indoor temperature in the data center.

[0209] 2. Thermal energy supply and demand mismatch constraints

[0210] P min ≤P(k)≤P max (35)

[0211]

[0212] Where: P(k) is the degree of mismatch between heat supply and demand at time k; p load (k) is the heat load demand of community users at time k; γ is the rated heat-to-electricity ratio of the cogeneration unit; P min , P max are the minimum and maximum values ​​of the allowed mismatch between heat supply and demand, respectively.

[0213]

[0214] Where: T n It is the time period of thermal and electric load mismatch during the system operation cycle; The longest time period of thermal and electrical load mismatch to ensure normal operation of the system within a complete cycle.

[0215] 3. Thermal comfort constraints for community users

[0216] The heat output by the data center waste heat compensation system to community users needs to ensure that their indoor temperature is within a certain thermal comfort range:

[0217]

[0218] Where: T user (k) is the indoor temperature of the community users at time k; and They are the minimum and maximum values ​​of standard indoor temperature respectively.

[0219] 4. Heat storage tank heat storage constraints

[0220] 0≤Q DC (k)≤Q max (39)

[0221] Where: Q max is the upper limit of heat storage of the phase change heat storage tank.

[0222] 4.3 Tube-MPC Control Strategy

[0223] In order to reduce the impact of data load uncertainty on the system during the optimization and control process, this paper adopts the Tube-MPC optimization and control method. Tube-MPC consists of a nominal model predictive controller and an auxiliary feedback controller, which transforms the control of the actual system into the control of the nominal system, so that the trajectory of the uncertain system is always in the Tube centered on the nominal trajectory. The actual uncertain data center waste heat compensation system is x(k+1)=Ax(k)+Bu(k)+Fr(k), and the constraints of the state variable x and the control variable u are x∈X,u∈U; the corresponding undisturbed nominal data center waste heat compensation system is z(k+1)=Az(k)+Bv(k), and the constraints of the state variable z and the control variable v are z∈Z,v∈V.

[0224] The nominal model predictive controller needs to control the nominal data center waste heat compensation system according to the objective function (32) to generate the economically optimal state trajectory {z(0),z(1),…,z(N)}, where z(N)∈Z N , N is the prediction time domain, Z N is the terminal contraction state constraint set, The nominal system constraints are more stringent than the actual system and can be expressed as:

[0225] Z=k1X,V=k2U (40)

[0226] Where: k1 and k2 are the adjustment parameters of the controller. By adjusting k1 and k2, the constraint set can be tightened.

[0227] The goal of the auxiliary feedback controller is to generate a set of control actions u to control the actual data center residual heat compensation system with uncertainty, minimizing the deviation between the actual data center residual heat compensation system state trajectory {x(0), x(1), ..., x(N)} and the optimal trajectory {z(0), z(1), ..., z(N)} obtained by the nominal model predictive controller. The objective function needs to ensure that the output and input (y and u) of the auxiliary feedback controller follow the output and input (g and v) of the nominal model predictive controller, and the constraints of the state and input are not tightened, which are X and U respectively. The objective function can be expressed as follows:

[0228]

[0229] Where: y = Cx, g = Cv; α and β are the weights of the controller output and input, respectively. α = 1 and β = 0.01 are usually selected to prioritize tracking the output generated by the nominal model predictive controller.

[0230] This paper uses MPT in Matlab to solve the optimization and control problem. The solution process within the complete optimization and control cycle is as follows: Figure 4 shown.

[0231] The data load of the data center in this article comes from the data released by Google. The typical daily data load change curve is as follows: Figure 5 As shown in the figure, the outdoor temperature is selected from a typical day in winter in northern my country, such as Figure 6 As shown. The number of servers configured in the data center is 1,500, the peak power is 600W, the silent power is 300W, the air-conditioning equipment capacity is 125kW, the server processing rate is 500 / s, the batch load accounts for 0.3, and the indoor temperature constraint of the data center is 20-26°C. The capacity of the waste heat storage tank is 300kWh, the thermal comfort range of community users is 18.5-24.0°C, and the heat supply and demand ratio range is 0.9-1.1. It is assumed that the ΔH caused by the fluctuation of data load will bring an uncertainty of ±1°C to the data center. The complete optimization and control cycle of the waste heat compensation system of the data center is 24h, the unit time period is 15min, and N k Take 96. Prediction time domain N=10.

[0232] The following three example scenarios are set for simulation verification:

[0233] Case 1: The waste heat from the data center is directly connected to the heating network without being regulated. The heating system uses the indoor temperature of community users as the only control target.

[0234] Example 2: Considering environmental cost factors, a data center waste heat compensation system is constructed and optimized.

[0235] Example 3: Considering the incentives of data center operators to community heating users and environmental cost factors, a data center waste heat compensation system is constructed and optimized.

[0236] Figure 7 , Figure 8 and Fig. 9 is the data load to be processed by the data center and the number of active servers at each moment in each case.

[0237] Depend on Figure 7It can be seen that there is a positive correlation between the number of active servers in the data center and the data load, which ensures sufficient processing capacity and meets the service quality requirements. When the data center uses its flexibility to participate in system regulation, it can postpone the processing time of batch processing loads, so that the data center has less excess heat when the heat load demand is low, and postpone the processing demand of batch processing loads to the period with higher heat load demand. The specific performance is as follows: Figure 8 and Fig. 9 Most of the batch loads are scheduled to be processed from 0:00 to 7:00 and from 19:00 to 24:00. Example 3 considers the incentives of data center operators to heating users. During the period of 8:00-18:00, the price of waste heat in the data center is reduced, the heat load demand of heating users increases, and the batch load increases. It can be seen that the proposed control model can flexibly arrange batch loads in time according to demand.

[0238] Fig.10 , Fig.11 and Fig.12 are the heat power and heat load in each case.

[0239] Depend on Fig.10 It can be seen that the overall heat supply of the system is not matched with the heat load demand of community users. From 22:00 to 7:00, the community electricity load decreases and the heat load increases. The "electricity determines heat" operation strategy causes the cogeneration unit to be unable to meet the heat demand, while the data center generates less waste heat at this time. From 11:00 to 18:00, the cogeneration unit can meet the system's heat demand, but the data center generates a large amount of waste heat during this period. In Example 1, there are 42.5% of the time periods in which the cogeneration unit and the data center waste heat still cannot meet the heat load demand. The average difference between the heat power and the heat load during this period is 0.44MW, and the maximum difference is 0.71MW; there are 34.8% of the time periods in which the heat power is much greater than the user's heat load demand. In Example 2, a data center waste heat compensation system is constructed and optimized and regulated to adjust the system output waste heat. The average difference between the heat power and the heat load during this period is 0.14MW, and the maximum difference is 0.33MW. Example 3 considers the price incentives that data center operators provide to community heating users based on Example 2. Heating users are more inclined to purchase waste heat when the waste heat price is low. Fig.12In the data center, from 8:00 to 18:00, the data center operator reduces the price of waste heat to promote waste heat consumption, and the heat demand of heating users increases; from 0:00 to 7:00 and 19:00 to 24:00, the operator increases the price of waste heat, and the heat demand of heating users decreases. Example 3 The average difference between thermal power and heat load in this period is 0.11MW, and the maximum difference is 0.26MW. It can be seen that after the control strategy proposed in this paper is used to control the waste heat compensation system of the data center, the output waste heat can be flexibly controlled, which makes up for part of the heat load demand that was not originally met by the system.

[0240] Since the reduction or transfer of waste heat from the data center and the uncertainty of data load will cause indoor temperature fluctuations for community users, it is necessary to investigate the indoor temperature conditions to ensure a comfortable heating experience. Fig.13 The indoor temperature simulation of community users in three examples.

[0241] Depend on Fig.13 It can be seen that in Example 1, the indoor temperature of community users is controlled as the only control target. The indoor temperature is between 20.4-22.3℃, with small fluctuations and high user comfort. Example 2 considers the time transferability of data center waste heat and cost factors, and the indoor temperature is between 19.6-22.7℃. Example 3 considers the time transferability of data center waste heat and the incentives and cost factors of data center operators for community heating users, and the indoor temperature is between 19.4-23.4℃. From the indoor temperature fluctuations of the three examples, it can be seen that data load uncertainty and regulating data center waste heat will increase the temperature fluctuation range, but the control strategy proposed in this article can ensure that the indoor temperature of community users is within the winter heating indoor temperature standard (18.5-24.0℃).

[0242] Data center indoor air node temperature T of the data center waste heat compensation system ia and server equipment rack temperature T r The trajectories of the two state quantities are as follows Fig.14 As shown. Fig.14 It can be seen that the state trajectory {x(0), x(1), …, x(N)} of the actual uncertain data center waste heat compensation system always remains in the Tube, and the center of the Tube is the economically optimal state trajectory {z(0), z(1), …, z(N)} generated by the nominal model predictive controller. The terminal state tightening constraint set ensures that in any prediction time domain, the terminal state x(N) of the actual uncertain data center waste heat compensation system always meets the system constraint requirements, that is, x(N)∈X N , ensuring the robustness of the system during operation.

[0243] To verify the effectiveness of Tube-MPC in handling system data load disturbances, the trajectories of temperature (state variable) and cooling power (control variable) generated by Tube-MPC and MPC are compared. Fig.15 shown.

[0244] Depend on Fig.15 (a) It can be seen that the indoor temperature of the data center is maintained close to the lower limit of 20℃ most of the time. Since the waste heat is captured from the condenser of the cooling system, the refrigeration system is regulated to generate as much cooling power as possible to provide enough heat to meet the thermal needs of community users. Even under the continuous influence of data load uncertainty interference, the Tube-MPC method can generate appropriate control actions for each time interval and successfully control the internal temperature of the data center within the allowable range. Although MPC can indirectly consider the impact of uncertainty by obtaining feedback from the state of the uncertain system, it still causes the DC indoor temperature to exceed the allowable range at certain moments. For example, at 6:00, 7:45 and 17:00, the indoor temperature of the data center is lower than the lower limit of 20℃. Fig.15 (b) shows the control input of the data center waste heat compensation system. Due to the continuous effect of data load uncertainty, the actual control input is not a fixed value. The data center waste heat compensation system based on Tube-MPC control can adaptively approximate the boundary of system uncertainty, making the control input curve smoother and maintained within a certain range.

[0245] The above is only a preferred embodiment of the present invention. It should be pointed out that, for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A control strategy for a data center waste heat compensation system considering adjustable data load, the specific steps of which are as follows: 1) Modeling server power considering the time-adjustable characteristics of data load 1.1) Data load model During operation, the data center will receive two types of data loads: interactive (IN) and batch processing (BA). The interactive load is sensitive to delay and requires the data center to process it immediately, so it does not have the ability to adjust the time; the batch processing load monomer has a large amount of computing data and the processing time can be from several minutes to several days. It has obvious delay tolerance characteristics and can be adjusted on the time scale. Under the guidance of the operator's incentives, data center users agree that BA-type loads are adjusted, provide specific load information after unified processing of requirements, and then participate in the optimization and regulation of the system. The amount of adjustment in BA-type loads is regarded as the response amount, which can be expressed as: Where: k∈{0,1,…,k,…,N k},N k is the total number of time periods in a complete regulation cycle; is the response of BA type load at time k; φ ba (k) is the BA load received by the data center at time k; β ba is the proportion of batch processing load in the total data load; is the total load received by the data center at time k, which will change with the data processing needs of the data center users and is uncertain. Its distribution range is The time transfer of BA type load is reflected in that the data load can be transferred from the current period to other periods, and data processing only needs to be completed within the specified time window. The model definition is as follows: Where: is the BA load response transferred from time k to time period [k+1,T], and the left side of the equation is the distribution of the adjusted BA load response in different time periods. In summary, the BA load λ processed by the data center at time k ba (k) and IN type load λ in (k) can be expressed as: In order to ensure the quality of service when processing data load, the response time for processing data load is required not to exceed the specified maximum delay that users can tolerate. Assuming that the data load is evenly distributed during runtime, according to the M / M / 1 queuing theory, it can be expressed as: Where: T qt Waiting time in queue for data load; n ser (k) is the number of servers in the power-on state at time k; T ht is the data load processing time; μ is the server processing rate; The maximum delay that the user can tolerate. Formula (1) to (8) analyze the time transferability of data load. Under the premise of satisfying the data load service quality, the data load of the data center can be adjusted on a time scale according to different goals. 1.2) Server Power Model The active power of a data center server is mainly determined by the number of servers powered on during the current period and the amount of data load being processed. Since data load has the characteristic of time transferability, the active power of the server can be changed by adjusting the data load, thereby changing the waste heat generated. For simplicity, this paper assumes that all servers in the data center are of the same model and that the control center evenly distributes the data load to all powered-on servers at any time. The active power of data center servers under different working conditions, the number of powered-on servers, and the server CPU utilization constraints can be expressed as: Where: P ser (k) is the active power of the server in the data center at time k; P idle is the silent power of a single server when it is not processing data load; P peak is the peak power; φ(k) is the data load at time k without considering uncertainty; μ is the server processing rate; Indicates the maximum number of available servers. max Indicates the upper limit of CPU usage of a single server. 2) Working model of data center waste heat compensation system The data center waste heat compensation system uses the data center waste heat as the heat source. In order to determine the waste heat recovery amount at each moment, the dynamic indoor temperature of the data center should be analyzed. The indoor temperature of the data center is affected by the heat emitted by the server, the cooling power of the refrigeration system, and the outdoor temperature. Considering that the data center building is usually a windowless closed structure, its building structure and servers are abstracted to form a resistant capacitance (RC) thermal network model. The RC heat network model of the data center abstracts the entities in the building into heat network nodes, uses the heat capacity of each node to represent the heat storage capacity, and the thermal resistance between nodes to represent the heat transfer path. The RC heat network model of the data center contains 5 nodes: ewo 、External wall inner node X ewi 、Inner wall node X iw 、Server Node X r and air node X ia . The relationship between the temperature of each node and the temperature of the adjacent node and the injected heat in the RC thermal network model of the data center can be expressed by a first-order differential equation: Where: m nodes are nodes to be described; T m and T n are the m and n node temperatures respectively; C m is the heat capacity of node m; R n,m is the thermal resistance between nodes n and m; H m is the external heat input to the m node; Ω c is the set of adjacent nodes of node m. According to formula (12), the first-order differential equations corresponding to the five nodes in the RC heating network are listed as shown in formulas (13)-(17). Where: T ewo is the temperature of the outer wall; T ewi is the temperature inside the exterior wall; T ia is the indoor air temperature; T iw is the inner wall temperature; T r is the server rack temperature; R oos is the thermal resistance of the exterior wall; R ewo is the half value of thermal resistance of the outer layer of the exterior wall; R ewi is the half value of the thermal resistance of the inner layer of the exterior wall; R ois is the thermal resistance of the inner surface of the exterior wall; Riws is the thermal resistance of the inner wall surface; R iw is the thermal resistance of the inner wall; R c is the thermal resistance of the ceiling; R r is the thermal resistance of the data center server equipment; C ewo is the heat capacity of the outer layer of the exterior wall; C ewi is the heat capacity of the inner layer of the exterior wall; C iw is the heat capacity of the inner wall; C r Heat capacity for data center server equipment; C ia is the heat capacity of the air in the computer room; T o is the outdoor air temperature, H e is the heat gain of the building envelope, T o and H e It is determined by the outdoor environment and directly affects the internal temperature of the data center. It can be calculated based on the indoor and outdoor environmental data. c is the cooling power of the refrigeration system at time k; H′ IT (k) is the waste heat generated by the server at time k. The waste heat generation of the server is calculated as follows: H′ IT (k) = H IT (k)+ΔH(k) (18) H IT (k) = η IT P ser (k) (19) Where: H IT (k) is the heat dissipated by the server when the uncertainty of data load is not considered at time k; ΔH is the change in server residual heat caused by data load uncertainty; η IT is the dissipation rate of the server. Since the power consumed by the server is almost completely converted into heat, the dissipation rate η IT Set to 1. In the cooling system of the data center, the condenser where heat is concentrated is a good location for waste heat recovery. The refrigerant absorbs the heat generated by the server in the evaporator, is cooled in the condenser, and releases the heat it carries. On this basis, according to the cooling power H of the cooling system at time k, c (k), the waste heat H recovered by the data center at each time can be calculated DC (k): H DC (k) = η DC H c (k) (21) Where: P acs (k) is the active power of the data center cooling system at time k; η acs is the energy efficiency coefficient of the refrigeration system; The capacity of air conditioning equipment configured for the data center; η DC Indicates waste heat recovery efficiency. The waste heat collected by the data center is usually low-grade waste heat and cannot be directly used for heating systems. In order to meet the prerequisites, the low-temperature waste heat needs to be upgraded through a heat pump, which can be expressed as: H HP (k) = H DC (k)+P HP (k) (22) H HP (k) = COP HP P HP (k) (23) Where: H HP (k) is the available high-grade thermal power output by the heat pump at time k; P HP (k) is the electrical power consumed by the heat pump at time k; COP HP is the coefficient of performance of the heat pump. The heat storage tank is used to store the waste heat collected from the data center. The heat energy Q stored in the recovery stage DC It can be expressed as: Where: k c It is the end time of the heat storage phase of the waste heat recovery system. During the working stage of the waste heat compensation system in the data center, the heat storage tank exchanges heat with the heating medium through the heat exchanger. This dynamic process can be expressed as: Where: M qms M is the mass of heat medium in the heat storage tank; g is the quality of heating medium; C qms C is the constant pressure specific heat capacity of the heat transfer medium in the heat exchanger connected to the heat storage tank; g is the constant pressure specific heat capacity of the heating medium; m qms is the mass flow rate of the heat exchange medium in the heat exchanger connected to the heat storage tank; m g is the mass flow rate of heating medium; T mi (k) is the inlet temperature of the heat exchanger connected to the heat storage tank at time k; T mo (k) is the outlet temperature of the heat exchanger connected to the heat storage tank at time k; T gim (k) is the inlet temperature of the heating medium that exchanges heat energy with the data center cooling system at time k; T gom (k) is the outlet temperature of the heating medium that exchanges heat energy with the data center cooling system at time k. After discretizing equations (13)-(17) and integrating them with equations (25) and (26), the spatial state equation of the data center waste heat compensation system can be obtained: Where: x = [T ewo T ewi T ia T iw T r T co T goc ] T is the state variable; u=[T o H e -H c H IT m csr m g ] T is the control variable; r=[ΔH] T is the disturbance variable. The coefficient matrices A, B, C and F of the data center waste heat compensation system are as follows. F = [0000100] T (31) 3) Data center waste heat compensation system control strategy This section proposes a control strategy for the waste heat compensation system in a data center. With the goal of minimizing the total cost of community users, Tube-MPC is used to optimize the system based on the price signals of various costs and the heat load requirements of community users. 3.1) Objective Function When optimizing the heating process, it is necessary to consider the electricity purchase cost W of community users. E (k), heat purchase cost W H (k) Environmental value cost W ENV (k) and the subsidy cost W for guiding data center users to actively respond to the subsidy IT (k), so the objective function can be expressed as: Where: W is the total daily operating cost, k0 is the starting time of optimization control. The costs can be expressed as: Where: c e (k) is the unit electricity price at time k; p e (k) is the power purchased by the community users at time k; c h(k) is the unit price of heat purchased at time k; p h (k) is the heat purchase power of community users at time k; q wh (k) is the unit price of waste heat in the data center at time k; p wh (k) is the waste heat power purchased by the user from the data center operator at time k; They are the CO2 emission intensity per unit of production capacity of traditional thermal power plants; is the environmental value of unit CO2; q ba (k) is the unit incentive given by the data center to the BA load at time k; q ba The value range of (k) is in It is the upper limit of the excitation for BA type load. 3.2) Constraints 1. Data center indoor temperature constraints: Where: They respectively represent the upper and lower limits of the allowed indoor temperature in the data center.

2. Thermal energy supply and demand mismatch constraints P min ≤P(k)≤P max (35) Where: P(k) is the degree of mismatch between heat supply and demand at time k; p load (k) is the heat load demand of community users at time k; γ is the rated heat-to-electricity ratio of the cogeneration unit; P min , P max are the minimum and maximum values ​​of the allowed mismatch between heat supply and demand, respectively. Where: T n It is the time period of thermal and electric load mismatch during the system operation cycle; The longest time period of thermal and electrical load mismatch to ensure normal operation of the system within a complete cycle.

3. Thermal comfort constraints for community users During the optimization and control process, the indoor temperature of community users should be guaranteed to meet the thermal comfort requirements of the human body: Where: T user (k) is the indoor temperature of the community users at time k; and They are the minimum and maximum values ​​of the standard indoor temperature respectively.

4. Heat storage tank heat storage constraints 0≤Q DC (k)≤Q max (39) Where: Q max is the upper limit of heat storage of the phase change heat storage tank. 3.3) Tube-MPC control strategy In order to reduce the impact of data load uncertainty on the system during the optimization and control process, this paper adopts the Tube-MPC optimization and control method. Tube-MPC consists of a nominal model predictive controller and an auxiliary feedback controller, which transforms the control of the actual system into the control of the nominal system, so that the trajectory of the uncertain system is always in the Tube centered on the nominal trajectory. The actual uncertain data center waste heat compensation system is x(k+1)=Ax(k)+Bu(k)+Fr(k), and the constraints of the state variable x and the control variable u are x∈X,u∈U; the corresponding undisturbed nominal data center waste heat compensation system is z(k+1)=Az(k)+Bv(k), and the constraints of the state variable z and the control variable v are z∈Z,v∈V. The nominal model predictive controller needs to control the nominal data center waste heat compensation system according to the objective function (32) to generate the economically optimal state trajectory {z(0),z(1),…,z(N)}, where z(N)∈Z N , N is the prediction time domain, Z N is the terminal contraction state constraint set, The nominal system constraints are more stringent than the actual system and can be expressed as: Z=k1X,V=k2U,k1,k2∈(0,1) (40) Where: k1 and k2 are the adjustment parameters of the controller. By adjusting k1 and k2, the constraint set can be tightened. The goal of the auxiliary feedback controller is to generate a set of control actions u to control the actual data center residual heat compensation system with uncertainty, minimizing the deviation between the actual data center residual heat compensation system state trajectory {x(0), x(1), ..., x(N)} and the optimal trajectory {z(0), z(1), ..., z(N)} obtained by the nominal model predictive controller. The objective function needs to ensure that the output and input (y and u) of the auxiliary feedback controller follow the output and input (g and v) of the nominal model predictive controller, and the constraints of the state and input are not tightened, which are X and U respectively. The objective function can be expressed as follows: Where: y = Cx, g = Cv; α and β are the weights of the controller output and input, respectively. α = 1 and β = 0.01 are usually selected to prioritize tracking the output generated by the nominal model predictive controller. This paper calls MPT in Matlab to solve the optimization control problem.

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